Math & Crop circles
Crop circles are (usually) circular patterns found in fields that are created by flattening the crop. Although they appear to be placed randomly, they are always near populated areas and cultural monuments. Cereologists (people that study crop circles - yes, they exist) have speculated a variety of reasons as to how crop circles are created including microwave radiation, atmospheric electricity from the ionosphere, people from society and even aliens!
But no matter what it is humans or indeed aliens creating these, it cannot be argued that crop circles have become one of the greatest art movements of human kind. Interestingly, individuals fluent in the language of mathematics have discovered a plethora of mathematical facts within these mysterious crop circles.
Consider the following picture of a crop circle at Barbury Castle in Wiltshire, England. To the average person, it may simply appear to be concentric circles of varying radii. But an astrophysicist named Michael Reed had discovered it embeds the first nine decimal digits of pi! Indeed, looking at the colored-in circle below, we observe the crop circle has been divided into 10 segments, each measuring exactly 36 degrees. The first digit of pi (3) is represented by the three innermost red segments. Then, we see a single green space with a dot inside it, representing the decimal place and first decimal digit of pi (1). Next are the four purple segements which represent the hundredths decimal place (4). This pattern continues and ultimately reveals pi rounded to nine decimal places: 3.141592654!
But no matter what it is humans or indeed aliens creating these, it cannot be argued that crop circles have become one of the greatest art movements of human kind. Interestingly, individuals fluent in the language of mathematics have discovered a plethora of mathematical facts within these mysterious crop circles.
Consider the following picture of a crop circle at Barbury Castle in Wiltshire, England. To the average person, it may simply appear to be concentric circles of varying radii. But an astrophysicist named Michael Reed had discovered it embeds the first nine decimal digits of pi! Indeed, looking at the colored-in circle below, we observe the crop circle has been divided into 10 segments, each measuring exactly 36 degrees. The first digit of pi (3) is represented by the three innermost red segments. Then, we see a single green space with a dot inside it, representing the decimal place and first decimal digit of pi (1). Next are the four purple segements which represent the hundredths decimal place (4). This pattern continues and ultimately reveals pi rounded to nine decimal places: 3.141592654!
Next, consider the crop crop circle below:
A mathematician named John Talbot had discovered something remarkable: within this crop circle was embedded the famous Euler's Identity! This is a famous identity that encapsulates the relationship between, arguably, the five most important numbers in mathematics:
- Euler's constant, e, which is approximately: 2.718281828459045
- The imaginary unit, i, which has an assigned value of sqrt(-1)
- The constant pi, which is approximately 3.1415926538
- The numbers 1 & 0
Now, this particular crop circle is broken up into 12 segments each measuring 30 degrees. Each of these segments contains arcs of concentric circles. Did you notice that each segment has exactly eight arcs? Well, John Talbot did and his interpretation was that these arcs correspond to digits in a binary number. Writing out the binary number for all the segments, you will obtain a string of 0's and 1's. Since we cannot interpret binary, Talbot decided to translate these strings into ASCII from which he discovered Euler's Identity. Although, we must add that it was not 'exact' - instead of the 'i' there was in fact 'hi', which led Talbot to believe that this particular crop circle was a prank performed be some (mathematically inclined) pranksters).
We leave you with this slideshow of various crop circles. See if you can find any mathematics in them!
We leave you with this slideshow of various crop circles. See if you can find any mathematics in them!
References:
http://plus.maths.org/content/os/latestnews/may-aug08/cropcircles/index
http://www.livescience.com/6546-beautiful-math-equation-crop-circle.html
http://plus.maths.org/content/os/latestnews/may-aug08/cropcircles/index
http://www.livescience.com/6546-beautiful-math-equation-crop-circle.html